If $x = 3$ is a root of the quadratic equation $x^{2} - m x + 5 = 0$ , find $m$

medium 2 marks Class 7 · Mathematics · Simple Equations

Answer

m=14/3

The correct answer is m=14/3 — This satisfies the given condition that one root is $3$ .

Step-by-step solution

Use Vieta’s formula: for $x^{2} - m x + 5 = 0$ , the sum of the roots equals $m$ and the product equals $5$ .
Let the other root be $r$ ; then $3 r = 5$ , so $r = \frac{5}{3}$ .
Sum of the roots: $3 + \frac{5}{3} = \frac{9}{3} + \frac{5}{3} = \frac{14}{3}$ .
Hence $m = \frac{14}{3}$ .
This satisfies the given condition that one root is $3$ .

Common mistake: Assuming the other root equals the constant term or misapplying the sign of the coefficient

Concept tested: Using Vieta's formulas in quadratic equations